Animation systems present animated characters in a three-dimensional virtual space. The virtual space includes a collection of mathematical models that define various objects, characters, scenery elements and the like, that can interact with each other. The animated characters move by programmatic changes in various parameters of the mathematical models. The virtual space is rendered, that is, converted from a mathematical model to a visual representation suitable for viewing by a user, and presented on a display to a viewer. Interactive animation can involve game players who control animated characters. Other animated characters may be programmatically controlled. Such characters can often mimic reality by showing awareness of other characters and objects in the virtual space. Further, certain classes of characters may have the ability to look at objects, aim at objects, attack objects, or otherwise interact with objects in the three dimensional virtual space.